Question
A train travels 240 km at a uniform speed. If the speed
of the train is increased by 20 km/h, it takes 1 hour less to cover the same distance. What is the original speed of the train?Solution
Solution: Let the original speed be x km/h. Time taken at original speed = 240/x hours. Time taken at increased speed = 240/(x + 20) hours. According to the problem: 240/x - 240/(x + 20) = 1. Cross-multiplying and simplifying gives: 240(x + 20) - 240x = x(x + 20) => 240 * 20 = x^2 + 20x => x^2 + 20x - 4800 = 0. Using the quadratic formula: x = [-20 ± √(20^2 + 4 * 4800)] / 2 x = 60 km/h. Correct answer: A) 60 km/h
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